Series Elastic Actuation:
Potential and Pitfalls∗
Jonathan W. Hurst and Alfred A. Rizzi
Daan Hobbelen
The Robotics Institute
Carnegie Mellon University
Pittsburgh, Pennsylvania
{jhurst, arizzi}@ri.cmu.edu
Department of Mechanical Engineering
Delft University of Technology
Netherlands
[email protected]
Abstract— In this paper we explore the space of design
freedoms associated with series elastic actuators. We specifically focus on the problem of damping, and evaluate through
simulation how inclusion of series damping can improve the
reliability and controllability of tasks involving force control
and impact. We explicitly build upon the pioneering work by
Pratt and colleagues at the MIT Leg Lab in the mid to late
1990s, and seek to define metrics for evaluating performance
of series elastic actuation systems. The conclusion demonstrates
the utility of including well tuned damping in such systems.
Index Terms— Actuator Force Control
I. I NTRODUCTION
It has long been understood that the inclusion of some
series elasticity in a robotic actuation system can be beneficial for tasks involving intermittent contact and/or impact.
There are many approaches for achieving desired levels of
compliance, ranging from constructing low inertia actuators
that are directly connected to load elements and controlled
by high bandwidth control systems (often relying on force
sensors to monitor load forces), to systems that explicitly
incorporate compliant elements to passively manage events
like impact loads. Crudely speaking, the range of approaches
can be classified based on a few parameters: the stiffness
of the transmission systems and physical links connecting
the actuator to the end effector, the energy storage capacity
of that transmission/linkage pair, and the damping ratio of
the transmission/linkage. All of these parameters are directly
involved in characterizing the effective impedance that the end
effector presents to the environment, and thus play a critical
role in how the entire robot will interact with its environment.
The property of energy storage is worth some additional
attention, since it can be used to classify systems into two
broad categories, those with and those without significant
passive dynamics. Systems that are capable of storing an
amount of energy comparable to that associated with a typical
impact can be tuned such that they passively exhibit a desired
behavior. Consider, for example, Raibert’s original hopping
machines[1]. These machines include compliant elements—
air springs—capable of capturing and returning the majority
∗ This work is partially supported by the Robotics Institute and Delft
University of Technology
of energy associated with hopping, allowing them to function with relatively minimal energy injection from a control
system. This strategy follows that of animals, who store gait
energy in springy tendons[2], [3], [4], [5]. More recently we
have begun developing a controlled compliant actuator that
we believe is capable of supporting Raibert-style running in
addition to a wide variety of other locomotion and contact
tasks [6], [7].
Over roughly the past decade, research centered at the MIT
Leg Lab has focused on a different type of series elastic actuation. They have sought to construct series elastic actuators
that have relatively small energy storage capability, but are
well suited to force control applications [8]. The actuators
developed at MIT utilize a very low-damping, series-spring
system with a moderate level of stiffness. Specifically, the
stiffness of these systems is not sufficiently soft to mimic
animal-like series stiffness and the associated energy storage
patterns typical for a running gait. However, in comparison
to a load cell (a common “compliant” element utilized in
force control applications) the devices are very soft. The MIT
style series elastic actuator (MIT-SEA) is primarily intended
for force control applications, and as a result of including a
moderate compliance between a highly geared actuator and
the load, is capable of dealing with rapidly changing force
loads. In comparison to a standard gearmotor, the risk of
transmission damage associated with impacts is drastically
reduced.
While better suited to force control tasks involving impact
than many options, the MIT-SEA introduces specific drawbacks to performance. Specifically, a poor match between
actuator and load inertias can lead to load oscillations that
are beyond the control bandwidth of the system, making it
difficult to reliably damp high-frequency oscillations arising
from impacts. The existing analysis of the MIT-SEA style
actuators incorrectly assumes that robot applications will
never violate these operating restrictions, making it difficult
to reliably predict performance in real world applications. The
applications for which the MIT-SEA is intended include both
force control tasks as well as tasks involving impact, and the
latter necessarily results in impulsive loads on the actuator
system. When we consider that the collisions producing these
loads are typically neither perfectly elastic nor perfectly in-
elastic, we realize that understanding the dynamics presented
by the actuator to the environment is critical in predicting
system behavior. Furthermore, as in all robotic applications,
we must consider that the load inertia is rarely constant, but
rather an actuator must be designed to perform well across a
wide range of load inertias, thus the system should perform
well both when the load inertia is significant in comparison
to the actuator’s inertia, as well as in the opposite case.
The remainder of this paper is dedicated to exploring the
performance capabilities and limitations of a series elastic
actuator system used for a force control task in the presence
of impacts. We will explore how design parameters can
be adjusted to mitigate the risk of undamped oscillations,
and evaluate the impact of such changes on performance.
We build directly on the prior work done at the MIT Leg
Lab by Robinson and colleagues[9], in an effort to better
understand how best to achieve the goal of realizing reliable,
safe, high-performance force actuation for general purpose
robot systems.
II. BACKGROUND
Fig. 1. A Series Elastic Actuator, with added damping. For comparison to
the MIT-style SEA, the damping magnitude may be set to zero.
Classical robots tend to use gearmotors for the most
rigid actuation possible, permitting good position control
of the end-effector. In the control literature, ”compliance”
or ”impedance” generally refers to behavior that is created
through software control of a rigid actuator[10]. There are
problems with this approach, especially for force control,
high-performance or highly dynamic systems. For example,
large disturbance torques on an electric motor will cause
the actuator impedance to dominate the overall behavior,
and a transmission will significantly worsen the effects[11].
Bandwidth limitations are caused not by controller sampling rate, but by fundamental aspects of the mechanical
system[12], [13]. As a solution to some of the problems, De
Schutter claims that all active force control methods require
a comparable degree of passive compliance in order to yield
a reasonable disturbance rejection capability[14]. In general,
the more compliance in the system, the better the force control
will be—for a given bandwidth limit, the force error due to
unforeseen object motions is inversely proportional to 1/k,
where k is the stiffness at the contact point.
Although series compliance has received recent attention
in the control literature, it is one of the oldest concepts in
actuation. Animals have series elasticity in most actuated
joints, implemented by placing muscles in series with springy
tendons. The series elasticity may be used for improved stability in a neural control system with time delay, and it is also
used for gait energy storage and work amplification during
walking and running gaits[15], [16]. A fishing rod is a series
elastic actuator, designed to be an extremely soft spring and
apply a consistent force on the hook, so the fish can’t escape
and the line won’t break. More recent implementations of
series elasticity include robot arms designed to reduce impact
forces in human interaction applications[17], and constant
force mechanisms which have no bandwidth limit[18].
The MIT-SEA includes a sensing and control design as well
as a mechanical design[9], [8]. A spring is placed in series
with a geared motor, and some load inertia is associated with
the end effector, as depicted in Figure 1. A PD controller
measures the deflection of the series spring, and commands
motor torques so the deflection of the spring will correspond
with the desired output force. The analysis is extensive, with
a general mathematical model that is independent of actuator
technology. Two case studies, an electromagnetic version and
a hydraulic version, are compared to simulation. The bandwidth of the MIT-SEA is defined by measuring the transfer
function between output force and desired force through a
range of frequencies. Tests are conducted by clamping the
load, and commanding positive and negative forces while
measuring and recording spring position. Output impedance,
which is essentially the transfer function between the output
force and load position, is measured by applying a constant
desired force and imposing the position of the load.
The recently demonstrated Series Damper Actuator is a
conceptually similar idea to the MIT-SEA[19]. An energy dissipating device is placed in series with the motor, rather than
an energy storage element as in the MIT-SEA. Oscillations do
not occur, as the only energy storage elements in the system
are mass inertias; any discrete change in end-effector velocity
results in an instantaneous applied force by the series damper.
The authors claim that the bandwidth of the system is high,
and the stability is good. One major drawback to this system
is that the motor must always burn energy to apply forces,
spinning at a specific rate to apply a specific force.
III. T HE P RIMARY I SSUE
An MIT-style series elastic actuator will apply forces
effectively and operate at a high bandwidth when the load
inertia is larger than the rotor inertia, and there are no motor
torque limits. Electric motor torques, of course, are limited,
which limits acceleration of the motor inertia and places
limitations on the bandwidth of the SEA. However, the ratio
of load to rotor inertias also affects the bandwidth, and can
be a severe limitation in real systems. When load inertia is
small compared to rotor inertia, an impulsive input at the load
causes relatively high-frequency oscillation that the software
controller cannot damp. The inertia of the rotor, along with
the motor torque limit, prevents rapid accelerations. This
limitation causes chatter during contact with a hard object,
or jiggling after a bump.
On pages 105 and 106 of David Robinson’s thesis[9],
he states that reflected rotor inertia is hardly ever large
compared to the load inertia; we contend that this assumption
is generally false. For the MIT Series Elastic Actuator, the
reflected inertia is 128 kg (stated on page 109). The actuated
link may be less than a few kilograms for a reasonable robot
arm or leg. When the end effector is in contact with the
ground or a larger body, then all of the assumptions and
analyses of the thesis are applicable; but before contact with
the ground or during the impact, the load inertia is only that of
the actuated link. Thus, robots built using the standard MITstyle SEA may be susceptible to contact chatter and other
oscillation effects that cannot be corrected through software
control.
This problem can be fixed in a number of different ways, or
by combining different methods. Our recommended solution
is to add a damper in parallel with the series spring. If
designed such that the spring-damper system is critically
damped for the load of the actuated link, then impacts or
impulses will result in a contact without chatter. Alternatively,
the rotor inertia can be reduced or the load inertia can be
increased until the two values match. Because the natural
oscillation frequency is the same between the motor and the
load, the software controller can effectively remove energy
from the system and damp unwanted oscillations. Another
solution is to reduce the stiffness of the series spring. While
this may reduce the likelihood of chatter on impact, it
also reduces the bandwidth of the system by requiring a
larger deflection for a given applied force, requiring faster
acceleration by the motor, which is limited by motor torque.
The load inertia on most robot manipulators, whether they
are legs or arms, is often variable during the task execution.
An arm may pick up heavy objects, a leg will support the mass
of the robot on the ground. This prevents a critically damped
mechanical system from remaining critically damped for all
tasks. However, if the load inertia becomes large compared to
the rotor inertia, then series damping is no longer necessary
for good performance.
IV. S IMULATION
To support our ideas that series damping can improve
performance in the presence of impulses and impacts, we
have simulated a series elastic actuator and subjected it to
both impacts and impulses. Our simulations are based closely
on those done in David Robinson’s thesis work, so our
simulations and his analyses can easily be compared. Our
simulation uses the following closed-loop electromagnetic
Series Elastic Actuator model, from page 94 of [9]:
Fl (s) =
(Kd s + Kp )Fd (s) − (mm s2 + bm s)Xl (s)
.
bm +ks Kd
mm 2
s + Kp + 1
ks s +
ks
The force applied to the load by the spring, Fl , is a function
of the desired force Fd and load motion Xl . The motor
inertia and damping mm and bm , the controller stiffness and
damping ks and kd , and the spring stiffness ks are all derived
from the physical device, and modified for various simulation
cases. Only a few changes to the basic model have been made.
Fig. 2.
The MIT Series Elastic Actuator model, copied directly from [9]
First, the parasitic motor damping term bm is not explicitly
included. It is effectively included by combining it with the
controller damping, kd . Also, we have added a motor torque
limit, which is an important realistic limitation. The system
is no longer linear, and closed-form solutions are no longer
feasible, so we have created all the graphs, except for the
Bode plots, through simulation.
We run three different simulations. The first is a test of
force bandwidth, identical to that done in [9]. The load
position is clamped, and the rate at which the actuator can
apply alternating positive and negative force is measured.
Figure 3 shows a Bode plot obtained through simulation of
the standard MIT-SEA, and also an MIT-SEA with added
damping in parallel with the spring, as in Figure 1. The
bandwidth of the system is slightly improved by adding
series damping, and we speculate that the improvement is
due to the force applied by the motor velocity. The motor
can now apply force by moving at some velocity as well
as by arriving at some position. This slight improvement is
relatively negligible, especially in comparison to removing the
series elements entirely; a standard gearmotor with no series
elasticity would perform much better, because the motor need
not accelerate to apply forces, and thus a motor torque limit
would not limit bandwidth. This particular test illustrates the
limitations of the SEA more than it illustrates any benefits.
The second and third simulations depict an impulse and
an impact on the load mass of the SEA. For each of these
simulations, four different cases are included:
1) SEA with torque saturation, rotor and load inertias
matched
2) SEA with no torque saturation, but with a small load
and a large rotor inertia
3) SEA with torque saturation, and a small load and a large
rotor inertia
4) SEA with torque saturation, small load, large rotor
inertia, and series damping as well as series elasticity
An impulse to the load inertia would instantaneously
change the velocity. Rather than apply a discrete velocity
change, we have given the load mass an initial velocity at
the beginning of the simulation. The actuator is commanded
10
Force on load as a result of an impulse
200
Fl / Fd (dB)
0
150
-10
100
-20
50
F [N]
series elasticity
series elasticity plus series damper
l
-30
45
0
Phase (deg)
-50
0
-100
Inertial match, torque sat.
Small load inertia, no torque sat.
Small load inertia, torque sat.
Small load inertia, torque sat., series damping
-150
45
-200
0
90
0
10
10
1
10
0.01
0.02
0.03
0.04
0.05
Time [s]
2
Frequency (Hz)
Fig. 3. Bode plot of the closed-loop transfer function of actual force on the
load over the desired force, showing the actuator’s force bandwidth in two
cases: the standard MIT-SEA and the MIT-SEA with added series damper.
The force bandwidth with the added series damper is slightly higher.
to apply zero force throughout the simulation, corresponding
with zero spring deflection. The resulting graph of force
applied by the series elements is shown in Figures 4 and 5. As
expected, the torque-limited actuator with large rotor inertia
and small load inertia oscillates significantly. By adding series
damping, the oscillation is nearly eliminated. The oscillation
is also greatly reduced by matching the load and rotor inertia.
Force on load as a result of an impulse
600
400
l
F [N]
200
0
-200
Where Fg is the reaction force, kg is the surface stiffness,
bg is the surface damping, and Xl is the end-effector position.
Fg can only be positive, and this equation only applies force
when the load mass has penetrated the ground, (xl > 0). An
inelastic collision would be approximated by adjusting bg ,
so this system is critically damped, and an elastic collision
would be approximated by setting bg to zero. Because most
collisions have some elastic component, and this elastic
rebound is the cause of contact chatter, we model some small
damping in the contact model so it is less than critically
damped.
The MIT-SEA starts some distance away from the surface,
and begins the simulation with a commanded force and an
initial velocity. At some point, the load comes into contact
with the wall. The load displacement is depicted in Figures 6
and 7. High-frequency oscillations result from the low-inertia
load bouncing between the surface elasticity and the MITSEA elasticity, and a low-frequency oscillation exists in case
of the higher load inertia. Only with a series damping element
is this oscillation eliminated.
Inertial match, torque sat.
Small load inertia, no torque sat.
Small load inertia, torque sat.
Small load inertia, torque sat., series damping
-400
-600
Fig. 5. A zoomed image of figure 4, more clearly showing the smaller
amplitude effects.
0
0.05
0.1
0.15
0.2
Time [s]
Fig. 4. Time response of the forces applied on the load by the series
elements during an external impulse on the load. Only inertial matching and
adding a series damper eliminates the oscillations.
Forces in the series elements resulting from contact are depicted in Figures 8 and 9. All cases settle on the commanded
force eventually, but it does take the case of the higher load
inertia about twenty times as long.
V. D ISCUSSION AND C ONCLUSIONS
An impact is modeled by adding a contact model to our
simulation:
Fg (s) = kg Xl (s) + bg sXl (s)
Depending on the task at hand, adding series compliance
can either help or harm the performance. But in the right application and with the right implementation, series compliance
is a major benefit. The MITSEA analysis and implementation
is extensive and informative, and as long as all of the
Load displacement as a result of impact
Force on load as a result of impact
2500
Inertial match, torque sat.
Small load inertia, no torque sat.
Small load inertia, torque sat.
Small load inertia, torque sat., series damping
0.1
-0.1
1500
F [N]
-0.2
l
Load displacement [mm]
2000
0
1000
-0.3
-0.4
500
Inertial match, torque sat.
Small load inertia, no torque sat.
Small load inertia, torque sat.
Small load inertia, torque sat., series damping
-0.5
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0
0.16
0
0.02
0.04
Time [s]
0.06
0.08
0.1
0.12
0.14
0.16
Time [s]
Fig. 6. Displacement of the load during an impact with a semi-elastic
surface, starting a certain distance away from the surface, given an initial
velocity and a command of 500N force. In three cases contact with the
surface causes chatter, where the contact is broken and reestablished several
times before settling. Only in the case of an added series damper does
the load settle without chatter. Although this figure shows relatively small
velocities and displacements for visibility reasons, similar effects occur at
higher speeds.
Fig. 8. Forces applied to the load by the series elements in case of an impact.
In all cases there is an overshoot of force due to the impact. Eventually all
cases settle at the commanded 500N force, the case with series damper
settles first and the case with large load inertia last.
Force on load as a result of impact
1000
Inertial match, torque sat.
Small load inertia, no torque sat.
Small load inertia, torque sat.
Small load inertia, torque sat., series damping
900
800
Load displacement as a result of impact
700
0.1
F [N]
0
l
Load displacement [mm]
600
500
400
-0.1
300
200
-0.2
100
0
-0.3
Inertial match, torque sat.
Small load inertia, no torque sat.
Small load inertia, torque sat.
Small load inertia, torque sat., series damping
-0.4
0
0.005
0.01
0.015
0.02
Time [s]
Fig. 7. A zoomed image of Figure 6, clearly showing the high-frequency
chatter of the non-damped systems, and the fast settle time of the damped
system.
assumptions are met, the analyses are accurate. However, the
assumptions are not met in many practical applications; the
most difficult problem is low load inertia paired with high
rotor inertia. By adding series damping, the control authority
over the system at all bandwidths is improved. Ideally, the
series elements should include a spring and a damper such
that the lowest expected load will be critically damped.
By eliminating unwanted oscillation through series damping
or other methods, series elasticity is an effective actuator
technology for force-control applications in which unexpected
impacts or fast disturbances are regularly encountered.
An interesting difference between a standard MIT-SEA and
one with added damping is that the series damper relates the
spring’s velocity to applied load force as well as the spring’s
0
0.005
0.01
0.015
0.02
Time [s]
Fig. 9. A zoomed image of Figure 8. The force fluctuations due to contact
oscillation are more clear in this image, where the lines wiggle.
position. The software controller can take advantage of this
additional coupling, and apply the desired force through a
combination of velocity and position. This is the most likely
explanation for the improved bandwidth on the SEA with
series damping.
The additional damping also causes a force spike at the
beginning of an impact. This force spike is presumably much
lower than that seen by a gearmotor on impact, but it is higher
than a standard MIT-SEA. Depending on the application, this
may or may not be acceptable. Perhaps the damping ratio
could be proportional to the spring deflection, to avoid the
initial spike in force, but still damp out the oscillations. We
will consider this as well as more sophisticated controllers in
future work.
This paper describes ideas that are supported by simulation,
but experiments on hardware would be much more convincing. We may perform hardware experiments in the near future
using existing haptic devices in the Biorobotics lab at Delft
University. In the intermediate future, we will build a device,
perform hardware experiments, and incorporate in a forcecontrol robotics application.
ACKNOWLEDGMENT
Thanks to Aaron Greenfield for discussion and advice
early in the writing process, and to Garth Zeglin for final
proofreading.
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